Approximating Clarke's subgradients of semismooth functions by divided differences
The aim of this paper is to demonstrate that the algorithm proposed by \textit{M. Studniarski} [Numer. Math. 55, 685--693 (1989; Zbl 0671.65044)] can be extended to a more general class of nonsmooth functions. That class is the one of semismooth functions introduced by \textit{R. Mifflin} [SIAM J. Control Optim. 15, 959--972 (1977; Zbl 0376.90081)]. A semismooth function has generalized gradients in the sense of Clarke and one-sided directional derivatives in every direction. The algorithm in the present paper works only for functions of two variables. Its convergence is demonstrated and some numerical tests are presented.
scientific article; zbMATH DE number 5145106
scientific article